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MS, University of Cincinnati, 2004, Engineering : Mechanical Engineering
Satellites flying in formation has been the focus of current research. Sometimes,there are issues with the amount of information available about the satellites. Due to hardware limitations, full measurements of relative positions and velocities of the spacecraft may not be available. In the long-term, the only information available might be the inter-satellite ranges between the satellites. The first part of the present work aims at the reconstruction of the trajectory of a satellite from this limited information, i.e., the time history of inter-satellite range. The present work deals with the case of three satellites in formation. One satellite is at the reference in a near circular orbit and the other two satellites trace Hill’s orbits relative to the reference. The geometry and phasing of one satellite is assumed to be known and the trajectory parameters of the other satellite relative to the reference are computed. Due to atmospheric drag there is a possibility that one of the satellites may drift and slip out of the formation. This may lead to a collision between the two satellites which might damage any appendages on the spacecraft like the antennas. The objective of the second part of the thesis is to devise a strategy to avoid the collision. The solution from the first part will be used to predict a possible collision in the future and a suitable thrusting technique will be applied to avoid the collision. The only collision scenario considered, in the present work, is 'tangential orbits'.


Dr. David Thompson (Advisor)


satellites; satellite formations; formation control; orbital mechanics

Jedrey, Richard M.Development of a Discretized Model for the Restricted Three-Body Problem
Master of Science, The Ohio State University, 2011, Aero/Astro Engineering
Spacecraft trajectory design is a science that requires high precision with little error. One of the most classic trajectory design problems is the restricted three-body problem. Two methods to develop the trajectory of a spacecraft under the influence of two celestial bodies are through the use of the equations of motion, and the patched-conic approximation. Popular tools such as MATLAB can be used to solve the equations of motion if great care is taken when selecting an ODE solver since the results are dramatically different between different solvers. As a result, these tools aren’t very robust and can create significant errors, so a different approach must be used for generalized scenarios when an exact solution for comparison is unavailable. The patched-conic approximation can be easily used in a program such as MATLAB, but its exclusion of one of the two celestial bodies at every point in the trajectory creates drawbacks and significant errors. To avoid the errors that exist when using the patched-conic approach, research was put into the development of a simple model that could propagate a spacecraft’s trajectory under the effect of two celestial bodies while being robust enough to code and solve in a widely available program such as MATLAB. This model acts as a modification to the patched-conic approach. Throughout the trajectory the effect of the primary celestial body of the system on the spacecraft was calculated, as in the patched-conic approach, however unlike the patched-conic approach this effect is not ignored when the spacecraft reaches the secondary body’s sphere of influence. Furthermore, the effect of the secondary body was also considered even when the spacecraft is outside the secondary body’s sphere of influence. Then, by applying a weighted average to the spacecraft’s radius and velocity components respective to each celestial body, an updated state would be created that would allow the model to accurately propagate the trajectory. This would be compared to a numerically generated ‘exact’ solution to determine the errors. Algorithms that propagate the spacecraft’s trajectory out with respect to both celestial bodies were created and tested, including the propagation of the secondary celestial body’s orbit itself. A scheme based on the geometry was used in an attempt to combine the spacecraft’s states with respect to both celestial bodies using a weighted average. This scheme was tested at multiple points throughout the trajectory using a variety of weights, but no attempts were met with any success. However, the routines propagating the trajectories of the celestial bodies and spacecraft were proven to work correctly, and an initial foundation in creating a scheme to combine the spacecraft’s state has been laid out.


Hayrani Oz, Dr. (Advisor); Rama Yedavalli, Dr. (Committee Member)


Aerospace Engineering; Engineering


orbital mechanics; spacecraft trajectories; three-body problem; three-body model; n-body problem; n-body model; discretized spacecraft;